In conventional lens generator apparatuses, the grinding and surface generation takes place in a grinding chamber into which a collet assembly of the tailstock projects. The collet assembly supports the lens blank; and the grinding chamber is provided with a cover plate, which permits access to the chamber. During operation of the lens generator apparatus, the lens blank sometimes becomes detached from the collet assembly; and some operators will attempt to retrieve the lens blank from the grinding chamber while the apparatus is in operation. An operator can be seriously injured if the operator's hand or arm inadvertently comes into contact with the high speed grinding tool. There are presently no asymmetrical lens generators whose operation may be instantaneously braked if the cover plate is opened or if the collet assembly is retracted.